




"""simple docstring"""




from itertools import count



def        a__					(							snake_case__ = 50							)		->   int:
			lowerCamelCase      =   [1] * min_block_length

			for n in count(snake_case__							):
						fill_count_functions.append(1							)

						for block_length in range(snake_case__			,					n + 1							):
									for block_start in range(n - block_length							):
												fill_count_functions[n] += fill_count_functions[
												    n - block_start - block_length - 1
												]

									fill_count_functions[n] += 1

						if fill_count_functions[n] > 1_00_00_00:
									break

			return n


if __name__ == "__main__":
					print(F"""{solution() = }""")









"""simple docstring"""




import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
lowerCAmelCase				:     List[str]					=				object()

# For specifying empty leaf dict `{}`
lowerCAmelCase				:     Any					=				object()



def        a__					(							snake_case__			,					snake_case__							)		->   List[Any]:
			lowerCamelCase      =   tuple((re.compile(x + """$"""							) for x in qs)							)
			for i in range(len(snake_case__							) - len(snake_case__							) + 1							):
						lowerCamelCase      =   [x.match(snake_case__							) for x, y in zip(snake_case__			,					ks[i:]							)]
						if matches and all(snake_case__							):
									return True
			return False



def        a__					(							snake_case__							)		->   str:
			def replace(snake_case__			,					snake_case__							):
						for rule, replacement in rules:
									if _match(snake_case__			,					snake_case__							):
												return replacement
						return val

			return replace



def        a__					(							)		->   Union[str, Any]:
			return [
			    # embeddings
			    (("transformer", "wpe", "embedding"), P("""mp"""			,					snake_case__							)),
			    (("transformer", "wte", "embedding"), P("""mp"""			,					snake_case__							)),
			    # atention
			    (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(snake_case__			,					"""mp"""							)),
			    (("attention", "out_proj", "kernel"), P("""mp"""			,					snake_case__							)),
			    (("attention", "out_proj", "bias"), None),
			    # mlp
			    (("mlp", "c_fc", "kernel"), P(snake_case__			,					"""mp"""							)),
			    (("mlp", "c_fc", "bias"), P("""mp"""							)),
			    (("mlp", "c_proj", "kernel"), P("""mp"""			,					snake_case__							)),
			    (("mlp", "c_proj", "bias"), None),
			    # layer norms
			    ((r"ln_\d+", "bias"), None),
			    ((r"\d+", r"ln_\d+", "scale"), None),
			    (("ln_f", "bias"), None),
			    (("ln_f", "scale"), None),
			]



def        a__					(							snake_case__							)		->   Optional[Any]:
			lowerCamelCase      =   _get_partition_rules()
			lowerCamelCase      =   _replacement_rules(snake_case__							)
			lowerCamelCase      =   {k: _unmatched for k in flatten_dict(snake_case__							)}
			lowerCamelCase      =   {k: replace(snake_case__			,					snake_case__							) for k, v in initd.items()}
			assert _unmatched not in result.values(), "Incomplete partition spec."
			return freeze(unflatten_dict(snake_case__							)							)



